Let $$G$$ be a weighted connected undirected graph with distinct positive edge weights. If every edge weight is increased by the same value, then which of the following statements is/are TRUE?

$$P:$$ Minimum spanning tree of $$G$$ does not change
$$Q:$$ Shortest path between any pair of vertices does not change

To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure to be used is:

Consider a weighted complete graph G on the vertex set {v1, v2, ..vn} such that the weight of the edge (vi, vj) is $$2|i-j|$$. The weight of a minimum spanning tree of G is: